Given:
The system of the linear equations is:
[tex]\begin{gathered} y=-x+2 \\ 3x-y=6 \end{gathered}[/tex]Required:
Find the solution to the system.
Explanation:
The given equations are:
[tex]\begin{gathered} y=-x+2.....(1) \\ 3x-y=6......(2) \end{gathered}[/tex]Substitute the value of y from equation (1) to equation (2).
[tex]\begin{gathered} 3x-(-x+2)=6 \\ 3x+x-2=6 \\ 4x-2=6 \\ 4x=8 \\ x=2 \end{gathered}[/tex]Substitute the value of x in equation (1) and find the value of y.
[tex]\begin{gathered} y=-2+2 \\ y=0 \end{gathered}[/tex]Thus the solution to the system is (2,0).
Final Answer:
The third option is the correct answer.